# Steam Entropy

## Basic steam thermodynamics and the entropy diagram

The entropy diagram for steam shows the relationships between

- Pressure
- Temperature
- Dryness Fraction
- Entropy

With two factors given - the others can be found in the diagram. The ordinates in the diagram represents the Entropy and the Absolute temperature.

The diagram consist of the following lines

- Isothermal line
- Pressure lines
- Lines of dryness fraction
- Waterline between water and steam
- Dry steam lines
- Constant volume lines

The total heat is given by the area enclosed by absolute zero base water line and horizontal and vertical line from the respective points.

An adiabatic expansion is a vertical line. An adiabatic process is expansion at constant entropy with no transfer of heat.

- Critical temperature of steam is
375 to 3,380^{o}C- Critical pressure is
217.8 atm

### Total Entropy of Steam

#### Entropy of Water

The change of entropy can be expressed as:

dS = log_{e}(T_{1}/T)(1)

where

T= absolute temperature (K)

The entropy of water above freezing point can be expressed as:

dS = log_{e}(T_{1}/273)(2)

#### Entropy of Evaporation

Change of Entropy during evaporation

dS = dL/T(3)

where

L= latent heat (J)

#### Entropy of wet steam

The entropy of wet steam can be expresses as:

dS = log_{e}(T_{1}/273) +ζ(L_{1}/T_{1})(4)

where

ζ= dryness fraction

#### Entropy of superheated steam

Change of entropy during super-heating can be expressed as

dS = c_{p}log_{e}( T/T_{1})(5)

where

c_{p}= specific heat capacity at constant pressure for steam (kJ/kgK)

The entropy of superheated steam can be expressed as:

dS = log_{e}( T_{1}/273 ) + L_{1}/T_{1}+ c_{p}log_{e}( T_{s}/T_{1})(6)

where

T_{s}= absolute temperature of superheated steam

T_{1}= absolute temperature of evaporation

### Water and Steam Entropy - Imperial Units

Temperature(^{o}F) | Absolute Pressure(psia) | Entropy (Btu/lb ^{o}F) | |
---|---|---|---|

Water | Steam | ||

0 | 0.0185 | -0.3243 | 2.330 |

10 | 0.0309 | -0.3141 | 2.283 |

20 | 0.0505 | -0.3038 | 2.238 |

30 | 0.0809 | -0.2936 | 2.195 |

32 (0 ^{o}C) | 0.0887 | 0.0000 | 2.187 |

40 | 0.1217 | 0.0162 | 2.159 |

50 | 0.1718 | 0.0361 | 2.126 |

60 | 0.2564 | 0.0555 | 2.094 |

70 | 0.3633 | 0.0746 | 2.064 |

80 | 0.5074 | 0.0933 | 2.035 |

90 | 0.6989 | 0.1116 | 2.008 |

100 | 0.9503 | 0.1296 | 1.982 |

110 | 1.277 | 0.1473 | 1.957 |

120 | 1.695 | 0.1647 | 1.933 |

130 | 2.226 | 0.1817 | 1.911 |

140 | 2.893 | 0.1985 | 1.889 |

150 | 3.723 | 0.2151 | 1.868 |

160 | 4.747 | 0.2314 | 1.848 |

170 | 5.999 | 0.2474 | 1.829 |

180 | 7.519 | 0.2632 | 1.811 |

190 | 9.350 | 0.2787 | 1.793 |

200 | 11.54 | 0.2941 | 1.776 |

210 | 14.12 | 0.3092 | 1.760 |

212 (100 ^{o}C) | 14.70 | 0.3122 | 1.756 |

220 | 17.20 | 0.3241 | 1.744 |

230 | 20.80 | 0.3389 | 1.729 |

240 | 24.99 | 0.3534 | 1.714 |

250 | 29.85 | 0.3678 | 1.700 |

*1 psi (lb/in*^{2}) = 6894.8 Pa (N/m^{2})*1 Btu/(lb*_{m}^{o}F) = 4186.8 J/ (kg K)